On distribution of Grubbs’ statistics in case of normal sample with outlier

2017 ◽  
Vol 61 (4) ◽  
pp. 72-88 ◽  
Author(s):  
L. K. Shiryaeva
Keyword(s):  
2006 ◽  
Vol 27 (2) ◽  
pp. 87-92 ◽  
Author(s):  
Willem K.B. Hofstee ◽  
Dick P.H. Barelds ◽  
Jos M.F. Ten Berge

Hofstee and Ten Berge (2004a) have proposed a new look at personality assessment data, based on a bipolar proportional (-1, .. . 0, .. . +1) scale, a corresponding coefficient of raw-scores likeness L = ΢XY/N, and raw-scores principal component analysis. In a normal sample, the approach resulted in a structure dominated by a first principal component, according to which most people are faintly to mildly socially desirable. We hypothesized that a more differentiated structure would arise in a clinical sample. We analyzed the scores of 775 psychiatric clients on the 132 items of the Dutch Personality Questionnaire (NPV). In comparison to a normative sample (N = 3140), the eigenvalue for the first principal component appeared to be 1.7 times as small, indicating that such clients have less personality (social desirability) in common. Still, the match between the structures in the two samples was excellent after oblique rotation of the loadings. We applied the abridged m-dimensional circumplex design, by which persons are typed by their two highest scores on the principal components, to the scores on the first four principal components. We identified five types: Indignant (1-), Resilient (1-2+), Nervous (1-2-), Obsessive-Compulsive (1-3-), and Introverted (1-4-), covering 40% of the psychiatric sample. Some 26% of the individuals had negligible scores on all type vectors. We discuss the potential and the limitations of our approach in a clinical context.


1973 ◽  
Vol 10 (1) ◽  
pp. 100-108 ◽  
Author(s):  
S. Beer ◽  
E. Lukacs

Yu. V. Linnik showed that certain transformations, given by Formulae (1.1), (1.6) and (1.7) transform a normal sample into itself. The transformations (1.1) and (1.7) apply to samples of size 2 while (1.6) admits an arbitrary sample size. It is also assumed that the population mean is zero.In the present paper the converse theorems are proven so that characterizations of the normal distribution are obtained. The problem leads to the functional equations (2.3) and (2.13) whose solution yields the desired results.


2018 ◽  
Author(s):  
Daniel P Cooke ◽  
David C Wedge ◽  
Gerton Lunter

Haplotype-based variant callers, which consider physical linkage between variant sites, are currently among the best tools for germline variation discovery and genotyping from short-read sequencing data. However, almost all such tools were designed specifically for detecting common germline variation in diploid populations, and give sub-optimal results in other scenarios. Here we present Octopus, a versatile haplotype-based variant caller that uses a polymorphic Bayesian genotyping model capable of modeling sequencing data from a range of experimental designs within a unified haplotype-aware framework. We show that Octopus accurately calls de novo mutations in parent-offspring trios and germline variants in individuals, including SNVs, indels, and small complex replacements such as microinversions. In addition, using a carefully designed synthetic-tumour data set derived from clean sequencing data from a sample with known germline haplotypes, and observed mutations in large cohort of tumour samples, we show that Octopus accurately characterizes germline and somatic variation in tumours, both with and without a paired normal sample. Sequencing reads and prior information are combined to phase called genotypes of arbitrary ploidy, including those with somatic mutations. Octopus also outputs realigned evidence BAMs to aid validation and interpretation.


1994 ◽  
Vol 26 (04) ◽  
pp. 855-875 ◽  
Author(s):  
Irene Hueter

Consider the convex hull of n independent, identically distributed points in the plane. Functionals of interest are the number of vertices Nn , the perimeter Ln and the area An of the convex hull. We study the asymptotic behaviour of these three quantities when the points are standard normally distributed. In particular, we derive the variances of Nn, Ln and An for large n and prove a central limit theorem for each of these random variables. We enlarge on a method developed by Groeneboom (1988) for uniformly distributed points supported on a bounded planar region. The process of vertices of the convex hull is of central importance. Poisson approximation and martingale techniques are used.


1991 ◽  
Vol 20 (2) ◽  
pp. 137-150 ◽  
Author(s):  
Terrel L. Templeman ◽  
Ray D. Stinnett

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